Donald Trump, the presumptive U.S. presidential nominee for the Republican Party, says the United States should "seriously" consider profiling Muslims in the fight against terrorism.

The call is the latest in string of statements Trump has made that have attracted wide criticism, both for their potential unconstitutionality but also for their potential to alienate large numbers of voters in the November general election.

Speaking June 19 on the current-affairs TV show Face The Nation, Trump argued that other countries like France already use profiling as a law-enforcement tool and "it's not the worst thing to do."

"I hate the concept of profiling, but we have to start using common sense,” he said.

Profiling is the government practice of targeting people for investigation based on factors such as their race, religion, or nationality.

In the United States, civil libertarians have called the practice discriminatory.

Trump made the comments in a discussion about Omar Mateen, the gunman who killed 49 people at a nightclub in Florida earlier this month. Mateen was Muslim.

In the past, Trump has said if elected president in November he "respectfully" would place mosques under surveillance. He's also proposed a temporary ban on foreign Muslims from entering the United States.

On Face The Nation, Trump was asked point-blank by the host if he was talking about increasing profiling of Muslims in America.

"Well, I think profiling is something that we're going to have to start thinking about as a country," he said.

He asserted that Israel practices racial profiling and that France also places mosques under surveillance.

"They're doing it in France. In fact, in some instances, they're closing down mosques. People don't want to talk about it. People aren't talking about it. But look at what they're doing in France. They're actually closing down mosques," he said.

The billionaire real-estate tycoon from New York has roiled the Republican Party in this year's presidential race, trouncing more than a dozen rivals in primary voting that concluded this month.

The party must still formally nominate him to be its candidate during its convention next month, but his incendiary remarks on Muslims, immigrants, women, same-sex marriage, and other positions have worried Republicans.

Some fear Trump could be headed for a landslide defeat at the hands of the presumptive Democratic nominee, former Secretary of State Hillary Clinton.

Recent polls show her holding onto a solid lead over Trump, and in some states where Trump would be expected to do well, her lead is even bigger.